Find the slope of the tangent to the curve $y=\frac{x-1}{x-2}, x \neq 2$ at $x=10$.

If the length of the subnormal at any point of the curve $y^n = a^{n-1}x$ is constant,then $n$ equals-

If the tangent drawn to the curve $(x^2+1)(y-3)=x$ at a point $P$,lying in the first quadrant,is a horizontal line,then the equation of the normal at the point $P$ is

If an equation of a tangent to the curve $y = \cos(x + y)$,where $-1 - \pi \le x \le 1 + \pi$,is $x + 2y = k$,then $k$ is equal to

If curves $\frac{x^2}{a^2} + \frac{y^2}{4} = 1$ and $y^3 = 16x$ intersect orthogonally,then $a^2$ equals:

If the angle between the curves $y^2=4x$ and $y=e^{-x/2}$ is $\theta$,then $\operatorname{cosec}^2(\theta/2)=$